The present invention relates generally to the field of force measurement using scanning probe microscopy (SPM) and, more particularly, to a force measurement system for determining the topography or composition of a local region of interest by means of scanning probe microscopy.
In this invention we use cartesian coordinate systems with perpendicular axes as the coordinate system of choice. Nevertheless, one may implement any other well-defined coordinate system including, for example, polar, cylindrical, or spherical coordinate system. The xe2x80x9cglobalxe2x80x9d coordinate system X Y Z 40 is fixed with the sample and the xe2x80x9clocalxe2x80x9d coordinate system Xtip Ytip Ztip 42 is fixed with the apex 45 of the tip 44 of the scanning probe 48. In general, the scanning probe tip apex 45 may have an arbitrary position and orientation with respect to the sample, therefore, the local coordinate system 42 also may have arbitrary position and orientation with respect to the global coordinate system 40, as shown in FIG. 1A. In a special case, the local 42 and global 40 coordinate systems may be aligned with respect to one another, as shown in FIG. 1B.
The origin of the local coordinate system 42 is at the apex 45 of the tip 44. The Ztip axis 46 is oriented along the length of the tip 44 and is perpendicular to a region of the oscillator 48 surface near the place where the tip 44 is attached. The Xtip axis 50 is parallel to the long axis of the oscillator 48. The Ytip axis 52 is transverse with respect to the Xtip axis 50 so as to form a right-handed cartesian coordinate system.
It is known that a dipole-dipole interaction occurs between pairs of atoms located in volumetric regions of the tip 44 and sample 54 when they are in proximity to each other. The associated force is called Van der Walls force. The resulting integrated effect encompasses all dipole-dipole interactions between pairs of atoms in sufficient proximity to generate a measurable interaction between the tip 44 and the sample 54. This resultant of the integrated dipole-dipole interaction is represented by a three-dimensional xe2x80x9ctip-sample interaction force vectorxe2x80x9d 56, as shown in FIG. 2A. A single point can be used to approximate the volumetric region near the tip apex 45, and a flat surface can be used to approximate the region of the sample 54 in proximity to the tip 44, as shown in FIG. 2B. If the surface of the sample 54 is horizontal (i.e., in the XY plane), the tip-sample interaction force vector 56 will be vertical. However, if the surface of the sample 54 is vertical (e.g., in the XZ plane), the tip-sample interaction force vector 56 will be horizontal. For a general orientation of the surface of the sample 54, the tip-sample interaction force vector 56 will have three non-zero components, corresponding to the three axes XYZ of the global coordinate system 40. The tip-sample interaction force vector F 56 can be represented either by its components Fx tip, Fy tip, Fz tip in the local coordinate system 42 or by its components FX, FY, FZ, in the global coordinate system 40.
In one possible mathematical representation, the 3xc3x971 vector functions ("PHgr"i, for (i=1, 2, 3, . . . ∞), of the spatial coordinates, (e.g., Xtip Ytip Ztip) represent mode shapes of the probe structure, and qi represent the corresponding generalized coordinates. In one instance of a classical modal analysis, the equations of motion of the probe are
Mjd2qj/dt2+Mjxcfx89j2qjxe2x88x92xcexa3i=1 to ∞Fijxe2x80x2qi=F0j
Where (j=1, 2, 3, . . . ∞), Mj is the modal mass, xcfx89j is the resonant frequency, and F0j is the static component of the generalized force corresponding to the tip-sample interaction force applied to the probe tip. The termxe2x88x92xcexa3i=1 to ∞Fijxe2x80x2qi can be interpreted as a negative spring force which alters the jth resonant frequency of the vibrating probe. The quantity Fijxe2x80x2 can be represented in terms of the mode shapes by
Fijxe2x80x2=[A]"PHgr"i(tip)xc2x7"PHgr"j(tip).
Where [A] is a 3xc3x973 coefficient matrix arising from classical modal analysis and the symbolxc2x7denotes an inner product of two vectors.
The vector [A] "PHgr"i (tip), derived from classical modal analysis, is an example of a more general vector quantity that we call a xe2x80x9cresultant surface force interaction.xe2x80x9d Our use of the term xe2x80x9cresultant surface force interactionxe2x80x9d is not limited to any particular physical origin of the tip-sample interaction force and may include, for example, both conservative and non-conservative tip-sample interaction forces.
FIG. 3A shows typical orientations of three selected mode shape vectors, evaluated at spatial coordinates corresponding to the apex 45 of a probe tip 44. In this example, "PHgr"1 (tip) 58 represents the direction in which the tip apex 45 moves when the main bending mode is excited; "PHgr"2 (tip) 60 represents the direction in which the tip apex 45 moves when the first torsional mode is excited; and, "PHgr"3 (tip) 62 represents the direction in which the tip apex 45 moves when the second bending mode is excited. For suitably chosen structural design of the probe 48 and tip apex 45 location, and for small-amplitude vibrations, "PHgr"3 (tip) 62, "PHgr"2 (tip) 60, and "PHgr"1 (tip) 58 are each substantially aligned with the unit vectors, itip 64, jtip 66, and ktip 68, respectively, and the modal coordinates q3, q2, q1 can be approximated by tip 44 displacements along the in the Xtip 50 Ytip 52 Ztip 46 axes, respectively. In this example, the resultants of the surface force interaction can be given a geometric interpretation as vectors aligned along the Xtip 50 Ytip 52 Ztip 46 axes.
The resultant surface force interaction vectors Fxe2x80x2x tip 70, Fxe2x80x2y tip 72, and Fxe2x80x2z tip 74 can, in some cases, be modeled by the three virtual springs with variable spring constants k1 76, k2 78, and k3 80 that are functions of the tip-surface distance, as shown in FIG. 3B. The vector Fxe2x80x2 82 shown in FIG. 3C is the sum of the three resultant surface force interaction vectors. As the force axis 84 and the distance axis 86 show in FIGS. 4A and 4B, the force-distance curve 88 shows that the resultant surface force is non-linear with respect to the tip-surface distance. Therefore, the modeled spring constants are also non-linear. However, for small amplitudes of vibration of the oscillator tip 44, the spring constants are linear with respect to the tip-surface distance. To maintain linear response, the oscillator 48 should vibrate with sufficiently small amplitude to keep the oscillator in a linear regime of operation, shown by area of measurement 90. Contrast that with area of measurement 92, used in tapping mode. Force axis 84 shows repulsive force 94 and attractive force 96.
The term xe2x80x9coscillator,xe2x80x9d as used in conjunction with the present invention, represents a scanning probe 48 for which multiple resonant modes are intended to be used for force sensing. The term xe2x80x9ccantileverxe2x80x9d refers to a scanning probe 48 for which only the primary bending (i.e., xe2x80x9ccantileverxe2x80x9d) mode is intended to be used for force sensing, even though, in general, the probe 48 structure would exhibit multiple resonant modal responses if excited at the appropriate driving frequencies.
The term xe2x80x9cforce sensorxe2x80x9d refers to the resonating oscillator 48 and its sensitivity to surface forces 82 associated with the tip-sample interactions. The purpose of the force sensor is to enable detection of the surface topology or composition by means of coupling the scanning probe tip 44 to the surface of the sample 54 via a tip-sample interaction force 82. In general, the interaction force 82 between the tip 44 and the sample 54 is a non-linear function of the tip-surface gap that includes the dipole-dipole interaction described above (which is conservative and hence describable by a potential), plus additional contributions from other conservative forces (e.g. electrostatic and magnetic forces) and non-conservative forces (e.g., meniscus forces and other forces due to surface contamination). However, whatever its origin in terms of atomic interactions, molecular interactions or other surface physics phenomena, the tip-sample interaction force vector 56 can still be represented by a vector composed of three generally non-zero components, corresponding to the three axes XYZ of the global coordinate system 40. Alternatively, the tip-sample interaction force 82 can be represented by a vector 56 composed of three generally non-zero components, corresponding to the three axes Xtip Ytip Ztip of the local coordinate system 42. Equal and opposite tip-sample interaction forces 82 act on the tip 44 and sample 54, respectively, consistent with Newton""s law of action and reaction.
xe2x80x9cForce sensingxe2x80x9d occurs when the surface force interaction alters the effective elastic restoring force associated with one or more resonant modes of the primary probe 48 structure so as to shift the respective natural frequencies of its resonant modes. The shifts in natural frequency can be sensed, for example, by monitoring either the amplitudes or phases of the respective modal oscillations.
When using the term xe2x80x9catxe2x80x9d in the claims herein to describe a positional relationship between two objects, the term xe2x80x9catxe2x80x9d is intended to be interpreted as meaning: (i) contacting the surface 54 or (ii) located near to but not contacting the surface 54. For example, when a SPM tip 44 is xe2x80x9catxe2x80x9d a sample surface 54 during a scan, the tip 44 may be contacting the surface 54 (as in contact or tapping mode testing), or the tip 44 may be located near to the surface 54, but without contacting the surface 54 (as in non-contact testing). As another example, when a distal end of a nanotube is xe2x80x9catxe2x80x9d a surface 54 of a semiconductor integrated circuit, the distal end of the nanotube may be contacting or tapping the surface 54, or the distal end of the nanotube may be located near the surface 54 without contacting the surface 54.
A scanning probe typically consists of a primary probe structure 48, (which may be either an oscillator or a cantilever) and a high aspect-ratio, sharply-pointed tip 44 extending from its end. The tip 44 is generally much less massive than the primary probe structure 48. The function of the primary probe structure is to provide one resonant mode (in the case of a cantilever) or more than one resonant mode (in the case of an oscillator), which are utilized for force sensing. Typically, the primary probe structure 48 is about 100 microns long by 30 microns wide by 2 microns thick. The function of the tip 44 is to rigidly couple the primary probe structure 48 to a relatively small volumetric region (the tip apex 45) which can be positioned so as to interact with a relatively small region of the sample 54 in proximity to the tip apex 45. Typically, the tip 44 is an inverted cone or a pyramid with its apex 45 pointing towards the sample surface 54. Ideally, the apex 45 of the tip 44 would be a single atom that couples with the sample surface 54 via the tip-sample force interaction. In reality, the apex 45 of the tip 44 typically has a radius of about 10 nanometers, and the cone-shaped or pyramid-shaped tip 44 is typically a few microns long.
In conventional scanning probe microscopy (SPM), the force sensor is only sensitive to the resultant of the surface force interaction Fxe2x80x2Z tip 74, in the Ztip 46, direction, as illustrated in FIGS. 5A and 5B. The other two components of the surface force interaction vector, Fxe2x80x2X tip 70 in Xtip 50 direction and Fxe2x80x2Y tip 72 in the Ytip 52 direction, are not detected in conventional scanning probe microscopy. The XYZ and Xtip Ytip Ztip coordinate systems are shown in FIGS. 5A and 5B as being aligned for ease of illustration. For conventional non-contact mode scanning, a SPM cantilever 48 is excited in its first bending mode with small amplitude, thereby causing the tip 44 to move within the attractive region of the surface force interaction profile. This region 90 is illustrated in FIG. 4A. In the conventional xe2x80x9ctappingxe2x80x9d mode, the amplitude of the cantilever 48 vibration is larger and the tip 44 dips in and out of both the attractive 96 and repulsive 94 regions of the surface force interaction region 92, as shown in FIG. 4B. A change in the tip-surface distance during the scanning process shifts the cantilever 48 resonance. A feedback loop uses the resonance shift to maintain either the amplitude or phase of the oscillation at a predetermined value. The output from the resulting scan is used to represent the topography or composition of the surface. Scanning of the probe in an XY raster plane while recording the response of the force sensor in Z-direction can be used to construct a three-dimensional profile of the surface 54.
There are two major consequences of the failure of conventional SPMs to detect the surface force interaction in multiple directions: (1) the vertical and horizontal distance scales will be different due to a diminished projection of the surface force interaction vector onto the vertical axis when the sample surface is not horizontal, and (2) there will be loss of force sensor sensitivity over highly sloped sample surfaces. To illustrate these points, we examine a tip 44 that is oriented in the Z-direction as it scans in the Y-direction over a horizontal surface 54 in the XY plane, as shown in FIG. 6. In this scenario, the surface force interaction 82 will be in the Z-direction when the surface 54 is horizontal. A conventional force sensor would drive the tip 44 at a constant surface force interaction set for scanning the horizontal surface. If the slope of the surface 54 changes, and with that the direction of the surface force interaction vector 82, the conventional force sensor would still only respond to the surface force interaction in the Z-direction 74. However, for a tilted surface, the surface force interaction in the Z-direction 74 is diminished by a factor equal to the cosine of the surface 54 slope angle representing the loss of the horizontal component 72 of the surface force interaction vector 82. The feedback controller of the conventional force sensor would keep the tip 44 over the sloped surface 54 at a constant surface force interaction level set for the horizontal surface 54. This misrepresentation will cause the tip 44 to be closer to a sloped surface 54 than to a horizontal surface 54, causing a distortion of the horizontal and vertical distance scales and a distortion of the surface 54 topography. This unwanted approach of the tip 44 to the surface 54 may also cause snapping of the tip to the surface. This snapping may damage the tip 44 or the sample 54.
Naturally, this problem is more emphasized when the surface is close to vertical or is vertical. For the case of a vertical surface, the surface force interaction occurs only in the horizontal direction. However, the conventional force sensor is only sensitive to a surface force interaction in the vertical direction. Therefore, the conventional force sensor loses its sensitivity over highly sloped surfaces and would not work for vertical or close to vertical surfaces.
One prior art embodiment, shown in FIG. 7, operates in a non-contact mode and has a cantilever 48 that resonates in the Z-direction and dithers (a non-resonant vibration) in the Y-direction. This approach is sufficient to enable force sensitivity in two directions. However, the force sensitivity in the lateral direction is not as good as the force sensitivity in the vertical direction. This is due to the use of dithering in the Y-direction rather than use of a distinct resonant mode that can provide higher force sensitivity. If the sample surface 54 is vertical, the vertical surface force interaction vanishes completely which renders the dithering approach ineffective.
Therefore, it would be desirable to operate a force sensor that provides force sensitivity in all three directions by means of distinct resonant modes.
All references cited herein are incorporated by reference to the maximum extent allowable by law. To the extent a reference may not be fully incorporated herein, it is incorporated by reference for background purposes, and indicative of the knowledge of one of ordinary skill in the art.
The problems and needs outlined above are addressed by the present invention. In accordance with one aspect of the present invention, a scanning probe microscopy (SPM) tool is provided. The SPM tool comprises an oscillator, an SPM tip, a mechanical actuator, a sensing system, and a feedback control system. The oscillator having the SPM tip extending therefrom. The mechanical actuator is adapted to hold the oscillator and position the SPM tip relative to a sample. The oscillator has a selected shape, dimensions ratio, and/or material composition such that the oscillator comprises a first resonant mode for a first direction, wherein a first resonance of the first resonant mode can be altered by a surface force interaction between the SPM tip and the sample in the first direction; and a second resonant mode for a second direction, wherein a second resonance of the second resonant mode can be altered by the surface force interaction between the SPM tip and the sample in the second direction. The sensing system is adapted to sense the alterations in the first and second resonances, is adapted to provide a first output based on the alterations in the first resonance, and is adapted to provide a second output based on the alterations in the second resonance. The feedback control system is adapted to control the actuator based on the first and second outputs. Nanotubes can be grown from the tip to provide more advantages.